Find the greatest common factor of $15$ and $42$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of both $15$ and $42$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}15 &=3\cdot5\\\\\\\\ 42&=2\cdot3\cdot7 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}15 &=3\cdot5\\\\\\\\ 42&=2\cdot3\cdot7 \end{aligned}$ Each number shares the factor ${3}$, so the GCF is ${3}$. The greatest common factor of $15$ and $42$ is $3$.